Related papers: Data Representation using the Weyl Transform

Weyl functions conveniently describe the evolution of wave coherences in periodic or quadratic potentials. In this work we use Weyl functions to study the ``Talbot-Lau effect'' in a time-domain matter-wave interferometer. A ``displacement…

In machine learning and neuroscience, certain computational structures and algorithms are known to yield disentangled representations without us understanding why, the most striking examples being perhaps convolutional neural networks and…

Motivated by the study of Weyl structures on conformal manifolds admitting parallel weightless forms, we define the notion of conformal product of conformal structures and study its basic properties. We obtain a classification of Weyl…

Oftentimes, patterns can be represented through different modalities. For example, leaf data can be in the form of images or contours. Handwritten characters can also be either online or offline. To exploit this fact, we propose the use of…

We prove a Weyl-type fractal upper bound for the spectrum of the damped wave equation, on a negatively curved compact manifold. It is known that most of the eigenvalues have an imaginary part close to the average of the damping function. We…

New type of tomographic probability distribution, which contains complete information on the density matrix (wave function) related to the Fresnel transform of the complex wave function, is introduced. Relation to symplectic tomographic…

Long-range interactions are a key resource in many quantum phenomena and technologies. Free-space photons mediate power-law interactions but lack tunability and suffer from decoherence processes due to their omnidirectional emission.…

Let B be a reductive Lie subalgebra of a semi-simple Lie algebra of the same rank both over the complex numbers. To each finite dimensional irreducible representation $V_\lambda$ of F we assign a multiplet of irreducible representations of…

We survey several generalizations of the Weyl algebra including generalized Weyl algebras, twisted generalized Weyl algebras, quantized Weyl algebras, and Bell-Rogalski algebras. Attention is paid to ring-theoretic properties,…

One-dimensional signal decomposition is a well-established and widely used technique across various scientific fields. It serves as a highly valuable pre-processing step for data analysis. While traditional decomposition techniques often…

The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the…

Let W be a Weyl group. We define a new basis for the Grothendieck group of representations of W. This basis contains on the one hand the special representations of W and on the other hand the representations carried by the left cells of W.…

Relational data representations have become an increasingly important topic due to the recent proliferation of network datasets (e.g., social, biological, information networks) and a corresponding increase in the application of statistical…

Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity…

Building on recent advances in representation learning for wireless channels, this work investigates the cost-benefit trade-offs of high-dimensional channel embeddings in practical systems. We benchmark multiple wireless representations:…

Starting from a generalization of Weyl's relations in finite dimension $N$, we show that the Heisenberg commutation relations can be satisfied in a specific $N-1$ dimensional subspace, and display a linear map for projecting operators to…

Feature representations, both hand-designed and learned ones, are often hard to analyze and interpret, even when they are extracted from visual data. We propose a new approach to study image representations by inverting them with an…

We provide the full classification, in arbitrary even and odd dimensions, of global conformal invariants, i.e., scalar densities in the spacetime metric and its derivatives that are invariant, possibly up to a total derivative, under local…

Theories have revealed the universality of the band tilting effect in topological Weyl semimetals (WSMs) and its implications for the material's physical properties. However, the experimental identification of tilted Weyl bands remains much…

There is a recent growing interest in applying Deep Learning techniques to tabular data, in order to replicate the success of other Artificial Intelligence areas in this structured domain. Specifically interesting is the case in which…